President Barack Obama, accompanied by Health and Human Services Secretary Kathleen Sebelius, announces the revamp of his contraception policy requiring religious institutions to fully pay for birth control, Friday, February 10, 2012, in the Brady Press Briefing Room of the White House in Washington.

Ever since the Obama administration included a requirement for no-cost contraceptive coverage in the Affordable Care Act last year, supporters and opponents have fought not only over the policy but also over how to frame the battle itself. For the most part, supporters have claimed that it’s about women’s health, while opponents have claimed that it centers on religious liberty.

In fact, the battle is about both. The administration’s announcement on Friday that religiously affiliated institutions are permitted to opt out of the contraception requirement strengthens religious liberty while safeguarding women’s health.

It’s important to keep both of these issues front and center when discussing the battle; it’s also important to be accurate. Here are a few facts.

Last Friday’s announcement came after the Obama administration spent more than a year weighing the various concerns of religious groups, health experts, women’s advocates, and others regarding the contraception requirement in the health care law. President Barack Obama’s recommendation went the extra mile in protecting religious liberty: He proposed an accommodation ensuring that religiously affiliated nonprofit organizations will not have to “contract, arrange, pay or refer for any contraceptive coverage to which they object on religious grounds.”

President Obama’s previous accommodation—announced in February 2012—would have accomplished the same thing. But the new mechanism—a separate insurance plan for contraception issued directly by insurance companies to employees, thereby completely eliminating the employer from the equation—leaves no room for doubt. At the same time, the president guaranteed that employees will still be able to receive contraception coverage with no co-pay, hopefully without complications.

The fact that last week’s accommodation didn’t satisfy all of its opponents should be no surprise, however, given their extreme demands. Exempting houses of worship and religious institutions from the requirement last year was not enough. Nor was allowing religiously affiliated nonprofits to opt out of the requirement. Opponents are dedicated to killing the contraception coverage requirement altogether.

One way they can accomplish this is by insisting on overly broad conscience exemptions, arguing that businesses and for-profit corporations should not be subject to the requirement. According to opponents, if the owners of Taco Bell morally object to contraception, they shouldn’t have to include it in their health plans, despite the fact that their employees rely on affordable contraception for their health and well-being.

Over the past year opponents have filed more than 40 lawsuits against the administration on behalf of religiously affiliated institutions that object to the contraception requirement. They also supported the Senate’s Blunt Amendment, which would have let employers refuse to provide coverage for a wide range of health services if those services violated the employers’ moral beliefs. If the Blunt Amendment had become law, for example, an employer would have been able to deny coverage for common services such as vaccinations and STD testing if he or she found them morally objectionable.

Hobby Lobby, an Oklahoma-based for-profit company, is one of 12 for-profit businesses that have sued the administration over the contraceptive-coverage regulation. Hobby Lobby’s owners are evangelical Christians who object to the requirement on religious grounds. With 500 stores and 13,000 workers, Hobby Lobby is a major employer. The exemption it is seeking is so broad that, if allowed, it would deny basic health services to thousands of employees and set a dangerous precedent that would affect millions of Americans.

Not only that—if such a broad religious exemption were granted to businesses, it could be applied in areas other than health care. Hotels and restaurants, for example, could potentially turn away same-sex couples if the owners believed homosexuality was morally objectionable. Redefining religious liberty in such a subjective way leads to a slippery slope that can only end in a chaotic heap, with businesses selectively choosing which laws they want to obey and misusing religion as an excuse to discriminate against those with whom they disagree.

But back to Friday’s announcement by President Obama: The good news is that support for the announcement came from a wide range of religious andwomen’s groups, which recognized the fact that the accommodation protects both religious liberty and women’s health. Miracles rarely occur in politics. But you could almost glimpse one in the statements of support issued by Planned Parenthood and the super-conservative Catholic League.

Never before have these groups agreed on anything similar to this—and perhaps they never will again. It’s worth noting this moment of harmony and clarity as we work to keep a clear light on these important issues—and as some seek to muddy the waters once again.

Sally Steenland is Director of the Faith and Progressive Policy Initiative at the Center for American Progress. Steenland, a best-selling author, former newspaper columnist, and teacher, explores the role of religion and values in the public sphere.